Finite Group Databasebeta

← C151×#15138 #50320063

Subgroups — C151×#15138 #50320063

Order 38656.

1762 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C151C212yesmaximal, complemented
2C2×#390×C151C211yesmaximal, characteristic
3C2×#390×C151C211yesmaximal, characteristic
4C2×#390×C151C211yesmaximal, characteristic
5C2×#389×C151C211yesmaximal, characteristic, complemented
6#1440×C151C212yesmaximal, complemented
7#1440×C151C212yesmaximal, complemented
8#1439×C151C212yesmaximal, complemented
9C4⋊#95×C151C211yesmaximal, characteristic, complemented
10C4⋊#95×C151C211yesmaximal, characteristic, complemented
11C4×#95×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2212yes—
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2212yes—
22C22×C22⋊C4×C151C2212yes—
23C22×C42×C151C2211yescharacteristic
24C22×C42×C151C2211yescharacteristic
25C22×C42×C151C2211yescharacteristic
26#397×C151—28no—
27#390×C151—24no—
28#390×C151—24no—
29#390×C151—24no—
30#389×C151—24no—
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2211yescharacteristic
35C2×#95×C151C2211yescharacteristic
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C2×#95×C151C2212yes—
39C2×#95×C151C2211yescharacteristic
40C25×C151C2312yes—
41C22×D4×C151—22no—
42C22×D4×C151—22no—
43C22×D4×C151—22no—
44C22×D4×C151—22no—
45C22×D4×C151—22no—
46C22×D4×C151—22no—
47C22×D4×C151D414yes—
48C23×C4×C151C2312yes—
49C23×C4×C151C2312yes—
50C23×C4×C151C2311yescharacteristic
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2312yes—
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2311yescharacteristic
55C23×C4×C151C2311yescharacteristic
56C23×C4×C151C2311yescharacteristic
57C23×C4×C151C2311yescharacteristic
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—24no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—24no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—42no—
69C2×C4⋊C4×C151D414yes—
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—24no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—24no—
76C2×C22⋊C4×C151—24no—
77C2×C22⋊C4×C151—24no—
78C2×C22⋊C4×C151—24no—
79C2×C22⋊C4×C151—24no—
80C2×C22⋊C4×C151—24no—
81C2×C22⋊C4×C151—24no—
82C2×C22⋊C4×C151—42no—
83C2×C22⋊C4×C151—42no—
84C2×C22⋊C4×C151—42no—
85C2×C22⋊C4×C151—42no—
86C2×C22⋊C4×C151—42no—
87C2×C22⋊C4×C151—42no—
88C2×C42×C151—22no—
89C2×C42×C151—22no—
90C2×C42×C151—22no—
91C2×C42×C151—22no—
92C2×C42×C151—22no—
93C2×C42×C151—22no—
94C2×C42×C151—22no—
95C2×C42×C151—22no—
96C2×C42×C151—22no—
97#95×C151—24no—
98#95×C151—24no—
99#95×C151—24no—
100#95×C151—22no—
101#95×C151—22no—
102#95×C151—22no—
103#95×C151—42no—
104#95×C151—42no—
105#95×C151D414yescomplemented
106C24×C151—22no—
107C24×C151—22no—
108C24×C151—22no—
109C24×C151—22no—
110C24×C151—22no—
111C24×C151—22no—
112C24×C151—22no—
113C24×C151—22no—
114C24×C151—22no—
115C24×C151—22no—
116C24×C151—22no—
117C24×C151—22no—
118C24×C151—22no—
119C24×C151—22no—
120C24×C151C2×D414yes—
121C24×C151C2411yescharacteristic
122C2×D4×C151—28no—
123C2×D4×C151—28no—
124C2×D4×C151—28no—
125C2×D4×C151—44no—
126C2×D4×C151—44no—
127C2×D4×C151—44no—
128C2×D4×C151—44no—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—22no—
155C22×C4×C151—22no—
156C22×C4×C151—22no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—22no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—22no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—22no—
172C22×C4×C151—22no—
173C22×C4×C151—22no—
174C22×C4×C151—22no—
175C22×C4×C151—22no—
176C22×C4×C151—22no—
177C22×C4×C151—22no—
178C22×C4×C151—22no—
179C22×C4×C151—22no—
180C22×C4×C151—22no—
181C22×C4×C151—22no—
182C22×C4×C151—22no—
183C22×C4×C151—22no—
184C22×C4×C151—22no—
185C22×C4×C151C2×D412yes—
186C22×C4×C151C2×D412yes—
187C22×C4×C151C2×D414yes—
188C22×C4×C151C2×D412yes—
189C22×C4×C151C2×D412yes—
190C22×C4×C151C2×D412yes—
191C22×C4×C151#4112yes—
192C22×C4×C151#4112yes—
193C22×C4×C151#4112yes—
194C22×C4×C151#4112yes—
195C22×C4×C151#4112yes—
196C22×C4×C151#4112yes—
197C22×C4×C151#4112yes—
198C22×C4×C151#4112yes—
199C4⋊C4×C151—28no—
200C4⋊C4×C151—48no—
201C4⋊C4×C151—44no—
202C4⋊C4×C151—44no—
203C22⋊C4×C151—48no—
204C22⋊C4×C151—48no—
205C22⋊C4×C151—48no—
206C22⋊C4×C151—48no—
207C22⋊C4×C151—48no—
208C22⋊C4×C151—48no—
209C42×C151—44no—
210C42×C151—44no—
211C42×C151—44no—
212C23×C151—24no—
213C23×C151—24no—
214C23×C151—24no—
215C23×C151—24no—
216C23×C151—24no—
217C23×C151—24no—
218C23×C151—24no—
219C23×C151—42no—
220C23×C151—42no—
221C23×C151—42no—
222C23×C151—42no—
223C23×C151—42no—
224C23×C151—42no—
225C23×C151—42no—
226C23×C151—42no—
227C23×C151—42no—
228C23×C151—42no—
229C23×C151—42no—
230C23×C151—42no—
231C23×C151—42no—
232C23×C151—42no—
233C23×C151—42no—
234C23×C151—42no—
235C23×C151—42no—
236C23×C151—42no—
237C23×C151—42no—
238C23×C151—42no—
239C23×C151—42no—
240C23×C151—42no—
241C23×C151—42no—
242C23×C151—42no—
243C23×C151—42no—
244C23×C151—42no—
245C23×C151—42no—
246C23×C151—42no—
247C23×C151C22×D411yescharacteristic
248C23×C151C22×D411yescharacteristic
249C23×C151C22×D411yescharacteristic
250C23×C151C2×#4111yescharacteristic
251C23×C151C2×#4111yescharacteristic
252C23×C151C2×#4111yescharacteristic
253C23×C151C2×#4111yescharacteristic
254C23×C151C2×#4111yescharacteristic
255C23×C151C2×#4111yescharacteristic
256C23×C151C2×#4111yescharacteristic
257C23×C151C2×#4111yescharacteristic
258C23×C151H(5,𝔽2)11yescharacteristic
259C23×C151H(5,𝔽2)11yescharacteristic
260C23×C151H(5,𝔽2)11yescharacteristic
261C23×C1512−1+411yescharacteristic
262D4×C151—416no—
263C2×C4×C151—24no—
264C2×C4×C151—22no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—22no—
271C2×C4×C151—22no—
272C2×C4×C151—22no—
273C2×C4×C151—24no—
274C2×C4×C151—22no—
275C2×C4×C151—22no—
276C2×C4×C151—22no—
277C2×C4×C151—22no—
278C2×C4×C151—24no—
279C2×C4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—42no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—42no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—42no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—42no—
312C2×C4×C151—42no—
313C2×C4×C151—42no—
314C2×C4×C151—42no—
315C2×C4×C151—42no—
316C2×C4×C151—42no—
317C2×C4×C151—42no—
318C2×C4×C151—42no—
319C2×C4×C151—42no—
320C2×C4×C151—42no—
321C2×C4×C151—42no—
322C2×C4×C151—42no—
323C2×C4×C151—42no—
324C2×C4×C151—42no—
325C2×C4×C151—42no—
326C2×C4×C151#12114yes—
327C2×C4×C151#12314yes—
328C2×C4×C151#12314yes—
329C2×C4×C151#12314yes—
330C2×C4×C151#12414yes—
331C2×C4×C151#12614yes—
332C2×C4×C151#12614yes—
333C22×C151—44no—
334C22×C151—44no—
335C22×C151—44no—
336C22×C151—44no—
337C22×C151—44no—
338C22×C151—44no—
339C22×C151—44no—
340C22×C151—82no—
341C22×C151—82no—
342C22×C151—82no—
343C22×C151—82no—
344C22×C151—82no—
345C22×C151—82no—
346C22×C151—82no—
347C22×C151—82no—
348C22×C151C2×#12111yescharacteristic
349C22×C151C2×#12311yescharacteristic
350C22×C151C2×#12311yescharacteristic
351C22×C151C2×#12311yescharacteristic
352C22×C151C2×#12411yescharacteristic
353C22×C151C2×#12611yescharacteristic
354C22×C151C2×#12611yescharacteristic
355C22×C151#52911yescharacteristic
356C22×C151#52911yescharacteristic
357C22×C151#52911yescharacteristic
358C22×C151#53211yescharacteristic
359C22×C151#53211yescharacteristic
360C22×C151#53211yescharacteristic
361C22×C151#54011yescharacteristic
362C22×C151#54011yescharacteristic
363C22×C151#54011yescharacteristic
364C22×C151#54211yescharacteristic
365C22×C151#54211yescharacteristic
366C22×C151#54211yescharacteristic
367C22×C151D4211yescharacteristic
368C22×C151D4211yescharacteristic
369C22×C151#54611yescharacteristic
370C22×C151#54611yescharacteristic
371C22×C151#54611yescharacteristic
372C22×C151#54711yescharacteristic
373C22×C151#54711yescharacteristic
374C22×C151#54811yescharacteristic
375C22×C151#55011yescharacteristic
376C22×C151#55011yescharacteristic
377C22×C151#55311yescharacteristic
378C22×C151#55311yescharacteristic
379C22×C151#55511yescharacteristic
380C22×C151#55611yescharacteristic
381C22×C151#55911yescharacteristic
382C22×C151#55911yescharacteristic
383C4×C151—42no—
384C4×C151—42no—
385C4×C151—42no—
386C4×C151—42no—
387C4×C151—44no—
388C4×C151—42no—
389C4×C151—42no—
390C4×C151—82no—
391C4×C151—82no—
392C4×C151#39718yescomplemented
393C2×C151—84no—
394C2×C151C2×#39711yescharacteristic
395C2×C151#242011yescharacteristic
396C2×C151#242211yescharacteristic
397C2×C151#242711yescharacteristic
398C2×C151#242811yescharacteristic
399C2×C151#244511yescharacteristic
400C2×C151#244511yescharacteristic
401C2×C151#244711yescharacteristic
402C2×C151#244811yescharacteristic
403C2×C151#249011yescharacteristic
404C2×C151#249111yescharacteristic
405C2×C151#251211yescharacteristic
406C2×C151#251311yescharacteristic
407C2×C151#264411yescharacteristic
408C2×C151#286011yescharacteristic
409#15138C15111yesmaximal, characteristic, direct product factor, Sylow
410C151#1513811yescharacteristic, direct product factor, Sylow
411C2×#397C2×C15112yescomplemented
412C2×#390C2×C15111yescharacteristic
413C2×#390C2×C15111yescharacteristic
414C2×#390C2×C15111yescharacteristic
415C2×#389C2×C15111yescharacteristic, complemented
416#1440C2×C15112yescomplemented
417#1440C2×C15112yescomplemented
418#1439C2×C15112yescomplemented
419C4⋊#95C2×C15111yescharacteristic, complemented
420C4⋊#95C2×C15111yescharacteristic, complemented
421C4×#95C2×C15111yescharacteristic, complemented
422C23×D4C22×C15111yescharacteristic
423C22×C4⋊C4C22×C15111yescharacteristic
424C22×C4⋊C4C22×C15111yescharacteristic
425C22×C4⋊C4C22×C15112yes—
426C22×C4⋊C4C22×C15111yescharacteristic
427C22×C22⋊C4C22×C15112yes—
428C22×C22⋊C4C22×C15112yes—
429C22×C22⋊C4C22×C15112yes—
430C22×C22⋊C4C22×C15112yes—
431C22×C22⋊C4C22×C15112yes—
432C22×C22⋊C4C22×C15112yes—
433C22×C42C22×C15111yescharacteristic
434C22×C42C22×C15111yescharacteristic
435C22×C42C22×C15111yescharacteristic
436#397—28no—
437#390—24no—
438#390—24no—
439#390—24no—
440#389—24no—
441C2×#95C22×C15112yes—
442C2×#95C22×C15112yes—
443C2×#95C22×C15111yescharacteristic
444C2×#95C22×C15111yescharacteristic
445C2×#95C22×C15111yescharacteristic
446C2×#95C22×C15112yes—
447C2×#95C22×C15112yes—
448C2×#95C22×C15112yes—
449C2×#95C22×C15111yescharacteristic
450C25C23×C15112yes—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4D4×C15114yes—
458C23×C4C23×C15112yes—
459C23×C4C23×C15112yes—
460C23×C4C23×C15111yescharacteristic
461C23×C4C23×C15111yescharacteristic
462C23×C4C23×C15111yescharacteristic
463C23×C4C23×C15112yes—
464C23×C4C23×C15111yescharacteristic
465C23×C4C23×C15111yescharacteristic
466C23×C4C23×C15111yescharacteristic
467C23×C4C23×C15111yescharacteristic
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4D4×C15114yes—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—24no—
511#95—24no—
512#95—24no—
513#95—42no—
514#95—42no—
515#95D4×C15114yescomplemented
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24C2×D4×C15114yes—
531C24C24×C15111yescharacteristic
532C2×D4—28no—
533C2×D4—28no—
534C2×D4—28no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4C2×D4×C15112yes—
596C22×C4C2×D4×C15112yes—
597C22×C4C2×D4×C15114yes—
598C22×C4C2×D4×C15112yes—
599C22×C4C2×D4×C15112yes—
600C22×C4C2×D4×C15112yes—
601C22×C4#41×C15112yes—
602C22×C4#41×C15112yes—
603C22×C4#41×C15112yes—
604C22×C4#41×C15112yes—
605C22×C4#41×C15112yes—
606C22×C4#41×C15112yes—
607C22×C4#41×C15112yes—
608C22×C4#41×C15112yes—
609C4⋊C4—28no—
610C4⋊C4—48no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C42—44no—
620C42—44no—
621C42—44no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C22×D4×C15111yescharacteristic
658C23C22×D4×C15111yescharacteristic
659C23C22×D4×C15111yescharacteristic
660C23C2×#41×C15111yescharacteristic
661C23C2×#41×C15111yescharacteristic
662C23C2×#41×C15111yescharacteristic
663C23C2×#41×C15111yescharacteristic
664C23C2×#41×C15111yescharacteristic
665C23C2×#41×C15111yescharacteristic
666C23C2×#41×C15111yescharacteristic
667C23C2×#41×C15111yescharacteristic
668C23H(5,𝔽2)×C15111yescharacteristic
669C23H(5,𝔽2)×C15111yescharacteristic
670C23H(5,𝔽2)×C15111yescharacteristic
671C232−1+4×C15111yescharacteristic
672D4—416no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4#121×C15114yes—
737C2×C4#123×C15114yes—
738C2×C4#123×C15114yes—
739C2×C4#123×C15114yes—
740C2×C4#124×C15114yes—
741C2×C4#126×C15114yes—
742C2×C4#126×C15114yes—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22C2×#121×C15111yescharacteristic
759C22C2×#123×C15111yescharacteristic
760C22C2×#123×C15111yescharacteristic
761C22C2×#123×C15111yescharacteristic
762C22C2×#124×C15111yescharacteristic
763C22C2×#126×C15111yescharacteristic
764C22C2×#126×C15111yescharacteristic
765C22#529×C15111yescharacteristic
766C22#529×C15111yescharacteristic
767C22#529×C15111yescharacteristic
768C22#532×C15111yescharacteristic
769C22#532×C15111yescharacteristic
770C22#532×C15111yescharacteristic
771C22#540×C15111yescharacteristic
772C22#540×C15111yescharacteristic
773C22#540×C15111yescharacteristic
774C22#542×C15111yescharacteristic
775C22#542×C15111yescharacteristic
776C22#542×C15111yescharacteristic
777C22D42×C15111yescharacteristic
778C22D42×C15111yescharacteristic
779C22#546×C15111yescharacteristic
780C22#546×C15111yescharacteristic
781C22#546×C15111yescharacteristic
782C22#547×C15111yescharacteristic
783C22#547×C15111yescharacteristic
784C22#548×C15111yescharacteristic
785C22#550×C15111yescharacteristic
786C22#550×C15111yescharacteristic
787C22#553×C15111yescharacteristic
788C22#553×C15111yescharacteristic
789C22#555×C15111yescharacteristic
790C22#556×C15111yescharacteristic
791C22#559×C15111yescharacteristic
792C22#559×C15111yescharacteristic
793C4—42no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—44no—
798C4—42no—
799C4—42no—
800C4—82no—
801C4—82no—
802C4#397×C15118yescomplemented
803C2—84no—
804C2C2×#397×C15111yescharacteristic
805C2#2420×C15111yescharacteristic
806C2#2422×C15111yescharacteristic
807C2#2427×C15111yescharacteristic
808C2#2428×C15111yescharacteristic
809C2#2445×C15111yescharacteristic
810C2#2445×C15111yescharacteristic
811C2#2447×C15111yescharacteristic
812C2#2448×C15111yescharacteristic
813C2#2490×C15111yescharacteristic
814C2#2491×C15111yescharacteristic
815C2#2512×C15111yescharacteristic
816C2#2513×C15111yescharacteristic
817C2#2644×C15111yescharacteristic
818C2#2860×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#397×C151C2semidirect
5. C2×#389×C151C2semidirect
6. #1440×C151C2semidirect
7. #1440×C151C2semidirect
8. #1439×C151C2semidirect
9. C4⋊#95×C151C2semidirect
10. C4⋊#95×C151C2semidirect
11. C4×#95×C151C2semidirect
105. #95×C151D4semidirect
392. C4×C151#397semidirect
409. #15138C151direct (N × H)
410. C151#15138direct (N × H)
411. C2×#397C2×C151semidirect
415. C2×#389C2×C151semidirect
416. #1440C2×C151semidirect
417. #1440C2×C151semidirect
418. #1439C2×C151semidirect
419. C4⋊#95C2×C151semidirect
420. C4⋊#95C2×C151semidirect
421. C4×#95C2×C151semidirect
515. #95D4×C151semidirect
802. C4#397×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#397×C1512
C2×#390×C1512
C2×#389×C1512
#1440×C1512
#1439×C1512
C4⋊#95×C1512
C4×#95×C1512
#15138151